In addition to the legal subtleties I'd like to take note of the *intent* of that consitutional requirement that only natural born citizens can be president. The obvious result of this provision is that no newcomer can become president. The president should be rooted in the United States. 

This must be seen in the historical context of a young, volatile democracy which felt -- not without reason -- under threat of a hostile takeover, politically or culturally. The office of the president was apparently considered powerful enough that the office holder could change the country. Immigration influx was continuous and huge. The provision guaranteed that the office holder would come from the "long-established", if such a thing existed, families. Such a member of the establishment would be less likely to alter the character of the emerging nation.

I'm not sure whether this is an argument supporting Cruz' eligiblility. One one hand, the requirements for his mother regarding the time she must have spent in the U.S. in order to make Cruz a citizen by birth support the notion that she was rooted in the U.S. But because there are no such requirements for Cruz himself, one could argue that he was for the intents and purposes of the consitutional provision -- the *president* should be rooted in the U.S. -- only as good as any naturalized alien.